Log-transforming *all* variables in panel regression

[Jonathan Quimby]

Hello all,

I wish to know whether log-transformation of my data is appropriate in this particular context.
Firstly, it's key to tell you that the goal of my analysis is only to establish a positive or negative (or no significant) relationship between certain independent variables and the dependent variables. In other words, the coefficient values are irrelevant, only the + or - is what i'm after.
Now for the statistics: Upon observing the variables (mostly economic ones), i noticed that some exhibit large Skewness and Kurtosis statistics.
This would prompt me to perform a log transformation on them; however, i remember reading somewhere that one cannot perform unit root tests on variables where some are log-transformed and others aren't.
Would it therefore be sound to simply log-transform *all* of the variables i'm working with here?

Thanks to anyone giving me their thoughts!

[Nick Cox]

In some fields for some problems, log transforming all variables is defensible. But that being possible depends on all values of each variable being positive and that being a good idea depends on much more than each variable's skewness and kurtosis. In fields I know about the motive is that a model

log Y = b_0 + b_1 log X_1 + b_2 log X_2 + ...

may prove useful

One simple class of examples is given by (0. 1) indicator variables, as there taking logarithms is not possible, and in any case any other transformation could not possibly change the absolute value of skewness and kurtosis. The reason is that any valid transformation just maps a distribution two spikes to another distribution with two spikes and the same distribution shape, modulo a possible reflection.

I think more concrete details are needed to give really good advice. The fleeting mention here of unit root tests suggests that you are only revealing part of what it is that you are trying to do.

[Jonathan Quimby]

Nick, thank you for your answer.

My worry - which i should have stated in the original post - is that i work with all sorts of data formats: ratios (scattered around 1), percentages, absolute values. I don't have the software on hand right now, but i think that the most "extreme" variables had kurtosis around 50 and skewness around 3.5, so transformation is absolutely necessary. Admittedly, I am now struggling to find sources that forbid LLC / IPS unit root tests from being penformed on data where some of it has been log-transformed while other hasn't. If this is untrue, perhaps the issue only applied for the cases where we would be trying to establish cointegration. Therefore, does this whole problem become moot if i was working with I(0) variables only? Conversely, if I(1) variables were concerned as well, the unit root tests would be still applicable (in the case that it truly does not matter that some variables are and others are not log-transformed).

I think more concrete details are needed to give really good advice

aside from what i have just added, is there anything else that i could add that would be of help? I'm at my wit's end.


(For future readers of this thread, i would also like to point out an enlightening thread which Nick has linked in his answer years ago, though it did not help me with this particular problem).

[Nick Cox]

Thanks for the link. I don't regard 2020 (the date of the linked thread) as that long ago. I don't agree that even kurtosis of 50 or so obliges you to transform, for all the reasons given here and there.

You've opened up on the time series aspect, where it really needs reactions from experts in those fields.